A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation

Lin Peng-cheng; Jiang Ben-xian

Volume 12 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(3): 259-268

Lin Peng-cheng, Jiang Ben-xian. A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation[J]. Applied Mathematics and Mechanics, 1991, 12(3): 259-268.

Citation:

Lin Peng-cheng, Jiang Ben-xian. A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation[J]. Applied Mathematics and Mechanics, 1991, 12(3): 259-268.

Citation:

Lin Peng-cheng, Jiang Ben-xian. A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation[J]. Applied Mathematics and Mechanics, 1991, 12(3): 259-268.

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A Singular Perturbation Problem for Periodic Bounday Partial Differentia! Equation

Fuzhou University, Fuzhou

Received Date: 1990-05-02
Publish Date: 1991-03-15

Abstract

Abstract

In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h²).
- elliptic-parabolic partial differential equation,
- singular perturbation problem,
- periodic boundary,
- difference scheme,
- uniform convergence

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References(6)

References

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[2]	林鹏程、江本话,奇异摄动的周期边界问题,应用数学和力学,8(1987),877-893
[3]	Kellogg,R.B.and A.Tsan,Analysis of some difference approximations for a singular perturbation problem without turning points,Math.Comp.,32(1987),1025-1039.
[4]	Il'in,A.M.,Difference scheme for a differential equation with a small parameter affecting the highest derivative,Mat.Zametki.,6(1969),237-248.
[5]	Емелъянов К.В.,О Разностной методе решения третъей краевой задачи для дифферендиалъного Уравнения с малым параметром при старшей производной,Ж.Бычисл Мамем.Физики,15,6(1975),1455-1463
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